Econ 409
B. Brown
Spring 2013
EXERCISE 5
Consider the following aggregate data in 1958 dollars (millions):
Year
Consumption
Disposable
Assets
Income
(
C
)(
D
)(
A
)
1946
127,235
147,089
728,310
1947
135,695
149,006
802,460
1948
145,757
165,261
889,960
1949
147,297
164,484
940,990
1950
154,992
180,434
953,090
1951
170,801
196,402
1,063,560
1952
181,179
205,950
1,151,240
1953
191,393
218,940
1,196,940
1954
197,958
223,308
1,225,210
1955
209,268
238,679
1,318,290
1956
222,854
253,903
1,427,030
1957
236,464
266,794
1,514,460
1958
246,247
273,516
1,555,700
1. Duesenberry considered the following model for aggregate consumption:
C
t
=
α
+
βD
t
+
u
t
where
u
t
is an unknown disturbance term.
a. Run an OLS regression based on this specification and report
ˆ
α
and
ˆ
β.
b. Making explicit the assumptions you are making, what are the properties of your estimates
ˆ
α
and
ˆ
β.
c. Test the null hypothesis that the marginal propensity to consume is one.
d. Discuss the properties of your test under the alternative that
β
is less than one.
2. Analternativemodelisbaseduponsavingbehaviorandcanbewritten:
S
t
=
α
+
βD
t
+
u
where
S
t
=
D
t
−
C
t
.
a. Obtain OLS estimates of
α
and
β.
b. What is the relationship between the slope coefficient here and in the preceding problem?
c. Rank (if possible) this regression and the previous regression.
d. Test the hypothesis that
β
in this model is one.
e. Calculate a 95% confidence interval for
ˆ
β
. What is the relationship of this interval to the
hypothesis test above.
1